Problem: Solve for $x$ and $y$ using substitution. ${2x+2y = 10}$ ${y = -4x+11}$
Answer: Since $y$ has already been solved for, substitute $-4x+11$ for $y$ in the first equation. ${2x + 2}{(-4x+11)}{= 10}$ Simplify and solve for $x$ $2x-8x + 22 = 10$ $-6x+22 = 10$ $-6x+22{-22} = 10{-22}$ $-6x = -12$ $\dfrac{-6x}{{-6}} = \dfrac{-12}{{-6}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {y = -4x+11}\thinspace$ to find $y$ ${y = -4}{(2)}{ + 11}$ $y = -8 + 11$ $y = 3$ You can also plug ${x = 2}$ into $\thinspace {2x+2y = 10}\thinspace$ and get the same answer for $y$ : ${2}{(2)}{ + 2y = 10}$ ${y = 3}$